The so-called "holy grail" of mathematics may have just been found. Shinichi Mochizuki, a professor at the Research Institute for Mathematical Sciences at Kyoto University, released a 500-page proof of the abc conjecture in number theory which involves the relationship between prime numbers, which I will attempt to describe as succinctly as possible below.
What exactly is the abc conjecture?
The ABC conjecture involves abc-triples: positive integers a,b,c such that a+b=c, a < b < c, a,b,c have no common divisors and c > rad(abc), the so-called radical of abc.* The ABC conjecture says that there are only finitely many a,b,c such that log(c)/log(rad(abc)) > h for any real h > 1. The ABC conjecture is currently one of the greatest open problems in mathematics. If it is proven to be true, a lot of other open problems can be answered directly from it.
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What exactly is the abc conjecture?
The ABC conjecture involves abc-triples: positive integers a,b,c such that a+b=c, a < b < c, a,b,c have no common divisors and c > rad(abc), the so-called radical of abc.* The ABC conjecture says that there are only finitely many a,b,c such that log(c)/log(rad(abc)) > h for any real h > 1. The ABC conjecture is currently one of the greatest open problems in mathematics. If it is proven to be true, a lot of other open problems can be answered directly from it.
- More Here
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